


The Beauty In Numbers

by afteriwake



Series: nongentorum [56]
Category: Star Trek: Alternate Original Series (Movies)
Genre: Beauty In Math, Bones Hates Math, Bones Is Entranced, Bones Learns To Like Math, Euler's Identity, M/M, Math Kink, Mathematics, Pre-Relationship, Spock Loves Math, The Most Beautiful Equation, can be read as platonic
Language: English
Status: Completed
Published: 2016-12-14
Updated: 2016-12-14
Packaged: 2018-09-08 11:13:11
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 900
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/8842510
Author URL: https://archiveofourown.org/users/afteriwake/pseuds/afteriwake
Summary: Math is one of the many things in the universe that Bones is not fond of, but it's one of the things that Spock can conceivably change his mind about when he explains why he finds Euler's Identity to be the most beautiful equation in existence.





	

**Author's Note:**

  * For [GreenSkyOverMe](https://archiveofourown.org/users/GreenSkyOverMe/gifts).



> So this is a combination of a Christmas gift for **squashbee** and a request fill for **GreenSkyOverMe** from [this headcanon](http://sleepymccoy.tumblr.com/post/148400904324/h-you-dont-know-me-but-i-hurt-my-leg-this) from **sleepymccoy** on Tumblr (" _Bones is bitching one night about how much maths is required for science. He quite likes science but finds that maths sucks the joy out of it. He’s going off for a bit, ranting at Spock, who interrupts to say he quite likes maths. Bones challenges Spock to name his favourite equation. Spock does so immediately, then spends ten minutes explaining in great detail, his eyes bright, the meaning and purpose of said equation. Bones still doesn’t like maths, but he does like watching Spock talk about it._ ") 
> 
> I got my information from the equation from Wikipedia, so I apologize if it isn't entirely correct. The Shakespeare quote is from Keith Devlin and the full quote is " _...like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence._ "

“That doesn’t even make sense,” Bones muttered, staring at the tablet in front of him, and then rechecking the calculations. He shook his head as he went over them a third time, finally finding his mistake, and then adjusted the medications needed. He glared at the tablet before stalking to the desk and nearly slamming it down as Spock moved over to him. 

“Do you need assistance, Doctor?” he asked.

Bones turned his glare to the Vulcan. He didn’t look smug, which was the only thing in his favor. More like concerned that he was going to throw a tantrum in the middle of the medbay, which was kind of _not_ in his favor. It made him want to wring the pointy eared bastard’s neck, but he reined in his temper. “I became a doctor to practice science, not math,” Bones said, his tone only sounding mildly irritated, though he was much more irritated than that. “There’s too much damn math in my job.”

“There are times that I prefer the math to the science,” Spock said, picking up the tablet and looking over the calculations.

“Checking over my work?” Bones asked, his voice tinged with an acidic tone.

“Admiring it,” Spock said, and Bones blinked. “I admire complex mathematical equations of all types. They are, in their way, a thing of beauty. Perhaps not to the standards that most people consider things to be beautiful, but I find a sense of flawlessness in most mathematical equations. There are some that I hold up as true works of art.”

Bones sat in his seat, giving Spock a look. He had never really heard him speak so passionately on anything before except his home planet. “Okay. So in your opinion, what mathematical equation should hang in at the Smithsonian or something?” he asked.

Spock looked up from the tablet, as though he was perplexed, that no one had ever asked that of him before. Then Bones watched as he slipped into the thought mode where he went into his deepest thinking mode, as though he was going over every mathematical equation he had ever been taught, and after what seemed like a moderately long time he spoke. “ _e iπ_ \+ 1 = 0, also known as Euler’s identity or Euler’s equation,” he said, picking up the tablet and writing the equation n it. “It was named after the Swiss mathematician Leonhard Euler. Many have said for hundreds of years that it is the prettiest equation, and I find myself agreeing with them.”

“Why?” Bones prodded, wanting to know how Spock saw beauty in math where all he saw was a massive headache.

“ _e_ is Euler’s number,” Spock explained, “which is the base of natural logarithms, and _i_ is the imaginary unit. This satisfies _i_ 2 = -1.”

Bones nodded. “Go on,” he said.

“Pi is, obviously, the ratio of the circumference of a circle to it’s diameter, or approximately 3.14159.”

“Yeah, everyone knows that,” Bones said.

“Euler’s identity is a form of Euler’s formula that is a special case of complex analysis which states that for any real number _x, __e ix_ equals cos _x_ plus _i_ sin _x_ , where the inputs of the trigonometric functions sine and cosine are given in radians. In particular, when _x_ equals _π_ , or one half-turn around a circle, then _e iπ_ equals cos _π_ plus _i_ sin _π_ , because cos _π_ equals -1 and sin _π_ equals 0, therefore it follows that _e iπ_ equals -1 + 0 _i_ , which yields Euler’s identity. It’s considered a piece of mathematical beauty because three of the basic arithmetic operations,addition, multiplication and exponentiation, occur exactly once, and it also links five fundamental mathematical constants.”__

__“What are they?” Bones asked, sounding interested despite himself._ _

__Spock lifted up his hand to count them down. “The number 0, which is the additive identity,” he said, lowering one finger. “The number 1, the multiplicative identity. The number _π_ , which is ubiquitous in the geometry of Euclidean space and analytical mathematics. The number _e_ , which is the base of natural logarithms, which occurs widely in mathematical analysis. Finally, the number _i_ , the imaginary unit of the complex numbers, a field of numbers that contains the roots of all polynomials that are not constants.”He paused and tilted his head. “It was once compared to a Shakespearean sonnet that, and I quote ‘captures the very essence of love,’ and I believe that is an apt description.”_ _

__Bones looked at him with a small grin on his face. “I didn’t think there was a real romantic bone in your body, Spock, but I guess I was wrong. I never thought math would be what brought it out of you.”_ _

__Spock frowned at Bones. “I do not know why you are confused, Doctor.”_ _

__Bones shook his head and took the tablet out of his hands, shaking his head. “It’s just...surprising, that’s all.” He stared at the equation. “I still hate math, though.”_ _

__When Bones looked up, he saw a small smile quirk at the edges of Spock’s lips. “Perhaps I can explain the beauty of some other equations and change your mind, Doctor.”_ _

__“I don’t see why not,” Bones said. “This was interesting. Spock gave him a nod and walked off, leaving Bones to hold the tablet. He may still hate math, but he _didn’t_ hate hearing Spock wax poetic about complex mathematical formulas._ _

__Go figure._ _


End file.
